SwePub - sökning: WFRF:(Asmussen Sören)

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1.	Asmussen, Sören, et al. (författare) A local limit theorem for random walk maxima with heavy tails 2002 Ingår i: Statistics and Probability Letters. - 0167-7152. ; 56:4, s. 399-404 Tidskriftsartikel (refereegranskat)abstract For a random walk with negative mean and heavy-tailed increment distribution F, it is well known that under suitable subexponential assumptions, the distribution pi of the maximum has a tail pi(x, infinity) which is asymptotically proportional to integral(x)(infinity)F(y,infinity) dy. We supplement here this by a local result showing that pi(x, x + z] is asymptotically proportional to zF(x,infinity). (C) 2002 Elsevier Science B.V. All rights reserved.
2.	Asmussen, Sören, et al. (författare) A Note on Skewness in Regenerative Simulation 2011 Ingår i: Communications in statistics. Simulation and computation. - : Informa UK Limited. - 0361-0918 .- 1532-4141. ; 40:1, s. 45-57 Tidskriftsartikel (refereegranskat)abstract The purpose of this article is to show, empirically and theoretically, that performance evaluation by means of regenerative simulation often involves random variables with distributions that are heavy tailed and heavily skewed. This, in turn, leads to the variance of estimators being poorly estimated, and confidence intervals having actual coverage quite different from (typically lower than) the nominal one. We illustrate these general ideas by estimating the mean occupancy and tail probabilities in M/G/1 queues, comparing confidence intervals computed from batch means to various intervals computed from regenerative cycles. In addition, we provide theoretical results on skewness to support the empirical findings.
3.	Asmussen, Sören (författare) A probabilistic look at the Wiener-Hopf equation 1998 Ingår i: SIAM Review. - 0036-1445. ; 40:2, s. 189-201 Tidskriftsartikel (refereegranskat)abstract Existence, uniqueness, and asymptotic properties of solutions Z to the Wiener-Hopf integral equation Z(x) = z(x) + integral(-infinity)(x) Z(x - y)F(dy), x greater than or equal to 0, are discussed by purely probabilistic methods, involving random walks, supermartingales, coupling, the Hewitt-Savage 0-1 law, ladder heights, and exponential change of measure.
4.	Asmussen, Sören, et al. (författare) An operational calculus for matrix-exponential disributions, with applicaions to a Brownian (q,Q) inventory model 1998 Ingår i: Mathematics of Operations Research. - 0364-765X. ; 23:1, s. 166-176 Tidskriftsartikel (refereegranskat)abstract distribution G on [math not displayed] is called matrix-exponential if the density has the form αeTz s where α is a row vector, T a square matrix and s a column vector. Equivalently, the Laplace transform is rational. For such distributions, we develop an operator calculus, where the key step is manipulation of analytic functions f(z) extended to matrix arguments. The technique is illustrated via an inventory model moving according to a reflected Brownian motion with negative drift, such that an order of size Q is placed when the stock process down-crosses some level q. Explicit formulas for the stationary density are found under the assumption that the leadtime Z has a matrix-exponential distribution, and involve expressions of the form f(T) where [math not displayed].
5.	Asmussen, Sören, et al. (författare) Asymptotics for sums of random variables with local subexponential behaviour 2003 Ingår i: Journal of Theoretical Probability. - 1572-9230. ; 16:2, s. 489-518 Tidskriftsartikel (refereegranskat)abstract We study distributions F on [0, infinity) such that for some T less than or equal to infinity F*(2)(x, x + T] similar to 2F(x, x + T]. The case T = infinity corresponds to F being subexponential, and our analysis shows that the properties for T < &INFIN; are, in fact, very similar to this classical case. A parallel theory is developed in the presence of densities. Applications are given to random walks, the key renewal theorem, compound Poisson process and Bellman-Harris branching processes.
6.	Asmussen, Sören, et al. (författare) Exact buffer overflow calculations for queues via martingales 2002 Ingår i: Queueing Systems. - 0257-0130. ; 42:1, s. 63-90 Tidskriftsartikel (refereegranskat)abstract Let tau(n) be the first time a queueing process like the queue length or workload exceeds a level n. For the M/M/1 queue length process, the mean Etaun and the Laplace transform Ee(-staun) is derived in closed form using a martingale introduced in Kella and Whitt (1992). For workload processes and more general systems like MAP/PH/1, we use a Markov additive extension given in Asmussen and Kella (2000) to derive sets of linear equations determining the same quantities. Numerical illustrations are presented in the framework of M/M/1 and MMPP/M/1 with an application to performance evaluation of telecommunication systems with long-range dependent properties in the packet arrival process. Different approximations that are obtained from asymptotic theory are compared with exact numerical results.
7.	Asmussen, Sören (författare) Extreme value theory for queues via cycle maxima 1998 Ingår i: Extremes. - 1572-915X. ; 1:2, s. 137-168 Tidskriftsartikel (refereegranskat)abstract The present state of extreme value theory for queues is surveyed. The exposition focuses on the regenerative properties of queueing systems, which reduces the problem to the study of the tail of the maximum $overline X( au)$ of the queueing process ${X(t)}$ during a regenerative cycle $ au$. For simple queues, methods for obtaining the distribution of $overline X( au)$ both explicitly and asymptotically are reviewed. In greater generality, the study leads to Wiener-Hopf problems. Extensions to queues in a Markov regime, for example, to those governed by Markov-modulated Poisson arrivals, are also considered.
8.	Asmussen, Sören, et al. (författare) Large deviations and fast simulation in the presence of boundaries 2002 Ingår i: Stochastic Processes and their Applications. - 1879-209X. ; 102:1, s. 1-23 Tidskriftsartikel (refereegranskat)abstract Let c(x) = inf {t > 0: Q(t) greater than or equal to x} be the time of first overflow of a queueing process 1001 over level x (the buffer size) and Z = P(T(X) less than or equal to T). Assuming that {Q(t)) is the reflected version of a Levy process {X(t)} or a Markov additive process, we study a variety of algorithms for estimating z by simulation when the event {tau(X) less than or equal to T} is rare, and analyse their performance. In particular, we exhibit an estimator using a filtered Monte Carlo argument which is logarithmically efficient whenever an efficient estimator for the probability of overflow within a busy cycle (i.e., for first passage probabilities for the unrestricted netput process) is available, thereby providing a way out of counterexamples in the literature on the scope of the large deviations approach to rare events simulation. We also add a counterexample of this type and give various theoretical results on asymptotic properties of Z=P(tau(x) less than or equal to T), both in the reflected Levy process setting and more generally for regenerative processes in a regime where T is so small that the exponential approximation for T(x) is not a priori valid.
9.	Asmussen, Sören (författare) Large deviations in rare events simulation: examples, counterexamples and alternatives 2002 Ingår i: Monte-Carlo and Quasi-Monte Carlo Methods 2000. Proceedings of a Conference. - 354042718X ; , s. 1-9 Konferensbidrag (refereegranskat)abstract When simulating small probabilities, say of order 10-6 or less, by importance sampling, an established principle is to choose the importance sampling distribution as close to the conditional distribution given the rare event as possible. Implementing this often leads into large deviations calculations and exponential change of measure. We survey some of the standard examples where this approach works and supplement existing counterexamples with new ones. Difficulties often arise as consequence of reflecting barriers and we present an algorithm which at least in simple cases is able to deal with this problem. Also the case of heavy-tailed distributions is considered
10.	Asmussen, Sören, et al. (författare) Loss rates for Lévy processes with two reflecting barriers 2007 Ingår i: Mathematics of Operations Research. - : Institute for Operations Research and the Management Sciences (INFORMS). - 0364-765X .- 1526-5471. ; 32:2, s. 308-321 Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract Let {Xt} be a Lévy process which is reflected at 0 and K>0. The reflected process {VtK} is constructed as VtK = V0K + Xt + Lt0 - LtK where{Lt0} and {LtK} are the local times at 0 and K, respectively. We consider the loss rate lK, defined by lK=E KL1K where E K is the expectation under the stationary measure K. The main result of the paper is the identification of lK in terms of K and the characteristic triplet of {Xt}. We also derive asymptotics of lK as K when EXt <0 and the Lévy measure of {Xt} is light-tailed.
11.	Asmussen, Sören, et al. (författare) Matrix-exponential distributions 2006 Ingår i: Encyclopedia of Statistical Sciences. ; 3 Tidskriftsartikel (refereegranskat)
12.	Asmussen, Sören, et al. (författare) On the tail of the waiting time in a Markov-modulated M/G/1 queue 2002 Ingår i: Operations Research. - : Institute for Operations Research and the Management Sciences (INFORMS). - 0030-364X .- 1526-5463. ; 50:3, s. 559-565 Tidskriftsartikel (refereegranskat)abstract We show that the "exponential decay parameter" of the waiting time in a Markov-modulated M/G/1 queue is no larger than that of the corresponding M/G/1 queue with "averaged" parameters, and we give a necessary and sufficient condition for equality. We also explore the effect of speeding up the modulation process. A key tool is a Markov-modulated fluid model.
13.	Asmussen, Sören, et al. (författare) Risk comparisons of premium rules: optimality and a life insurance study 2003 Ingår i: Insurance: Mathematics and Economics. - 1873-5959. ; 32:3, s. 331-344 Tidskriftsartikel (refereegranskat)abstract Consider a risk Y-1 (x) depending on an observable covariate x which is the outcome of a random variable A with a known distribution, and consider a premium p(x) of the form p(x) = EY1 (x) + etap(1) (x). The corresponding adjustment coefficient gamma is the solution of E exp{gamma[Y-1(A) - p(A)]} = 1, and we characterize the rule for the loading premium p(1)((.)) which maximizes gamma subject to the constraint Ep(1) (A) = 1. In a life insurance study, the optimal p(1)(*)((.)) is compared to other premium principles like the expected value, the variance and the standard deviation principles as well as the practically important rules based on safe mortality rates (i.e., using the first order basis rather than the third order one). The life insurance model incorporates premium reserves, discounting, and interest return on the premium reserve but not on the free reserve. Bonus is not included either. (C) 2003 Published by Elsevier Science B.V.
14.	Asmussen, Sören, et al. (författare) Russian and American options under exponential phase-type Lévy models 2004 Ingår i: Stochastic Processes and their Applications. - 1879-209X. ; , s. 79-111 Tidskriftsartikel (refereegranskat)abstract Consider the American put and Russian option (Ann. Appl. Probab. 3(1993)603; Theory Probab. Appl. 39 (1994)103; Ann. Appl. Probab. 3(1993)641) with the stock price modeled as an exponential Lévy process. We find an explicit expression for the price in the dense class of Lévy processes with phase-type jumps in both directions. The solution rests on the reduction to the first passage time problem for (reflected) Lévy processes and on an explicit solution of the latter in the phase-type case via martingale stopping and Wiener-Hopf factorization. The same type of approach is also applied to the more general class of regime switching Lévy processes with phase-type jumps.
15.	Asmussen, Sören, et al. (författare) Stationarity properties of neural networks 1998 Ingår i: Journal of Applied Probability. - 1475-6072. ; 35:4, s. 783-794 Tidskriftsartikel (refereegranskat)abstract A neural model with N interacting neurons is considered. A firing of neuron i delays the firing times of all other neurons by the same random variable theta((i)), and in isolation the firings of the neuron occur according to a renewal process with generic interarrival time Y-(i). The stationary distribution of the N-vector of inhibitions at a firing time is computed, and involves waiting distributions of GI/G/1 queues and ladder height renewal processes. Further, the distribution of the period of activity of a neuron is studied for the symmetric case where theta((i)) and Y-(i) do not depend upon i. The tools are probabilistic and involve path decompositions, Palm theory and random walks.
16.	Asmussen, Sören (författare) Subexponential asymptotics for stochastic processes : extremal behavior, stationary distributions and first passage probabilities 1998 Ingår i: Annals of Applied Probability. - 1050-5164. ; 8:2, s. 354-374 Tidskriftsartikel (refereegranskat)abstract Consider a reflected random walk Wn+1 = (W-n +X-n)(+), where X-o, X-1,... are i.i.d. with negative mean and subexponential with common distribution F. It is shown that the probability that the maximum within a regenerative cycle with mean mu exceeds x is approximately mu (F) over bar(x) as x --> infinity, and thereby that max (W-o,..., W-n) has the same asymptotics as max(X-o,...,X-n) as n --> infinity. In particular, the extremal index is shown to be theta = 0, and the point process of exceedances of a large level is studied. The analysis extends to reflected Levy processes in continuous time, say, stable processes. Similar results are obtained for a storage process with release rate r(x) at level x and subexponential jumps (here the extremal index may he any value in [0, infinity]); also the tail of the stationary distribution is found. For a risk process with premium rate r(x) at level x and subexponential claims, the asymptotic form of the infinite-horizon ruin probability is determined. It is also shown by example [r(x) = a + bx and claims with a tail which is either regularly varying, Weibull- or lognormal-like] that this leads to approximations for finite-horizon ruin probabilities. Typically, the conditional distribution of the ruin time given eventual ruin is asymptotically exponential when properly normalized.
17.	Jonsson, Erland, 1946, et al. (författare) A Dependability Measure for Degradable Computing Systems 1992 Rapport (övrigt vetenskapligt/konstnärligt)abstract This paper deals with the problem of finding a comprehensive dependabilitymeasure or figure of merit for computing systems. Dependability is a term usedfor a general description of a systems trustworthiness in non-quantitative terms. Itis commonly described by a number of aspects, like reliability, availability, safetyand security. Quantitative measures are conveniently used for e.g. reliability andavailability, but are rare for security.However, it is felt that a more general measure of a system’s dependability wouldbe of great interest and could be used for system evaluations, design trade-offs etc.In order to achieve this, we adopt a generalized view that facilitates a recompilationof the dependability aspects into fewer and more general qualities. Key issues forthe generalization are the concepts of degradability and service. A degraded serviceis the result of the discontinuation of one or several subservices, yielding a systemthat operates on a reduced service level.A vectorized measure based on Markov processes is suggested, and mathematicaldefinitions are given. The measure describes the expected time a system willbe operating at a certain service level, and also the probability that this level bereached. By means of applying the concept of reward rate to each service level, aneven more simplified figure of merit can be calculated.Normally, when making reliability calculations, an assumption of exponentialfailure rates for system components is made. Sometimes this assumption is notrealistic and we outline how phase-type distributions can be used to cope with thissituation.Finally, two different schemes for the calculation of the measure is given. First,a hierarchical procedure feasible for small systems and calculations by hand is presented.Second, a general procedure based on matrix calculus is given. This procedureis suitable for complicated systems. It is also general in the sense that it maybe used for measures extended to repairable systems.
18.	Jonsson, Erland, 1946, et al. (författare) A practical dependability measure for degradable computer systems with non-exponential degradation 1994 Ingår i: IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processe - SAFEPROCESS 1994. ; Vol. 1, s. 231-237 Tidskriftsartikel (refereegranskat)abstract This paper proposes a vectorized measure for a set of behavioural dependability attributes. The measure is based on Markov processes and is intended for practical dependability trade-offs. It describes the system performance on a number of service levels. Thus, it is possible to merge attributes such as reliability, safety and performability into one single quality. Whereas reliability describes the functional fulfillment of a system, performability reflects its ability of functional degradation. The safety attribute handles a class of failures with catastrophic consequences and can be accommodated by means of introducing two or more service levels for a failed system.Many systems exhibit time-dependent degradation rates and non–exponential lifetimes. This situation can be handled by means of applying phase–type assumptions and introducing some additional states to the system, which would allow us to remain within the universe of Markov modelling.
19.	Jonsson, Erland, 1946, et al. (författare) An Attempt to Quantitative Modelling of Behavioural Security 1995 Ingår i: Proceedings of the 11th International Information Security Conference - IFIP/SEC 1995. ; addendum, s. 44-57 Tidskriftsartikel (refereegranskat)abstract This paper suggests a quantitative approach to security, and specifically to a security-concept, which is regarded as an attribute of dependability together with reliability, availability and safety. We note that security is a more complex attribute of dependability than are the other three, and that it can therefore be split into preventive and behavioural aspects. We show that, in addition to availability, confidentiality could be used to denote a new type of behavioural aspect of dependability. Integrity is interpreted in terms of fault prevention, and is not directly related to system behaviour. A practical measure for behavioural dependability attributes including confidentiality is defined. Due to the dependability viewpoint of security that we take, a measure could be derived using traditional reliability methods, such as Markov modelling. The measure is meant for practical trade-offs within a class of computer systems. The measure quantifies system performance on user-specified service levels, which may be operational or failed. Certain levels may be related to confidentiality degradations or confidentiality failures. A simple Reference Monitor example is given to illustrate the use of the measure. The calculation method is then extended to handle situations with non–exponential failure rates, which is the normal case in security applications, by means of using phase–type modelling. This is illustrated by introducing malicious software, such as a Trojan Horse into the Reference Monitor.
20.	Lindgren, Georg, et al. (författare) Stationary processes 2004 Ingår i: Encyclopedia of Actuarial Sciences. - 0470846763 - 9780470846766 Bokkapitel (övrigt vetenskapligt/konstnärligt)

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