| 1. |
- Bartoszek, Krzysztof, 1984-, et al.
(författare)
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On the Time Behaviour of Okazaki Fragments
- 2006
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Ingår i: Journal of Applied Probability. - Cambridge : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 43, s. 500-509
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Tidskriftsartikel (refereegranskat)abstract
- We find explicit analytical formulae for the time dependence of the probability of the number of Okazaki fragments produced during the process of DNA replication. This extends a result of Cowan on the asymptotic probability distribution of these fragments.
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| 2. |
- Britton, Tom, et al.
(författare)
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Epidemics on random graphs with tunable clustering
- 2008
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 45:3, s. 743-756
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Tidskriftsartikel (refereegranskat)abstract
- In this paper a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large outbreak in the epidemic. We investigate how these quantities vary with the clustering in the graph and find that, as the clustering increases, the epidemic threshold decreases. The network is modeled by a random intersection graph, in which individuals are independently members of a number of groups and two individuals are linked to each other if and only if there is at least one group that they are both members of.
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| 3. |
- Britton, Tom, et al.
(författare)
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The early stage behaviour of a stochastic SIR epidemic with term-time forcing
- 2009
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 46:4, s. 975-992
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Tidskriftsartikel (refereegranskat)abstract
- The general stochastic SIR epidemic in a closed population under the influence of a term-time forced environment is considered. An 'environment' in this context is any external factor that influences the contact rate between individuals in the population, but is itself unaffected by the population. Here 'term-time forcing' refers to discontinuous but cyclic changes in the contact rate. The inclusion of such an environment into the model is done by replacing a single contact rate λ with a cyclically alternating renewal process with k different states denoted {A(t)}t≥0. Threshold conditions in terms of R⋆ are obtained, such that R⋆ > 1 implies that π, the probability of a large outbreak, is strictly positive. Examples are given where π is evaluated numerically from which the impact of the distribution of the time periods that Λ(t) spends in its different states is clearly seen.
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| 4. |
- Ekström, Erik, 1977-
(författare)
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Bounds for perpetual American option prices in a jump-diffusion model
- 2006
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 43:3, s. 867-873
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Tidskriftsartikel (refereegranskat)abstract
- We provide bounds for perpetual American option prices in a jump diffusion model in terms of American option prices in the standard Black–Scholes model. We also investigate the dependence of the bounds on different parameters of the model.
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| 5. |
- Ekström, Erik, et al.
(författare)
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Optimal stopping of a Brownian bridge
- 2009
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Ingår i: Journal of Applied Probability. - 0021-9002 .- 1475-6072. ; 46:1, s. 170-180
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Tidskriftsartikel (refereegranskat)abstract
- We study several optimal stopping problems in which the gains process is a Brownian bridge or a functional of a Brownian bridge. Our examples constitute natural finite-horizon optimal stopping problems with explicit solutions.
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| 6. |
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| 7. |
- Hammarlid, Ola
(författare)
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Tools to estimate the first passage time to a convex barrier
- 2005
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Ingår i: Journal of Applied Probability. - 0021-9002 .- 1475-6072. ; 42:1, s. 61-81
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Tidskriftsartikel (refereegranskat)abstract
- he first passage time of a random walk to a barrier (constant or concave) is of great importance in many areas, such as insurance, finance, and sequential analysis. Here, we consider a sum of independent, identically distributed random variables and the convex barrier cb(n/c), where c is a scale parameter and n is time. It is shown, using large-deviation techniques, that the limit distribution of the first passage time decays exponentially in c. Under a tilt of measure, which changes the drift, four properties are proved: the limit distribution of the overshoot is distributed as an overshoot over a linear barrier; the stopping time is asymptotically normally distributed when it is properly normalized; the overshoot and the asymptotic normal part are asymptotically independent; and the overshoot over a linear bather is bounded by an exponentially distributed random variable. The determination of the function that multiplies the exponential part is guided by consideration of these properties.
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| 8. |
- Holst, Lars
(författare)
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A NOTE ON EMBEDDING CERTAIN BERNOULLI SEQUENCES IN MARKED POISSON PROCESSES
- 2008
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 45:4, s. 1181-1185
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Tidskriftsartikel (refereegranskat)abstract
- A sequence of independent Bernoulli random variables with success probabilities a/(a + b + k - 1), k = 1, 2, 3, ... , is embedded in a marked Poisson process with intensity 1. Using this, conditional Poisson limits follow for counts of failure strings.
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| 9. |
- Holst, Lars
(författare)
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Counts of failure strings in certain Bernoulli sequences
- 2007
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 44:3, s. 824-830
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Tidskriftsartikel (refereegranskat)abstract
- In a sequence of independent Bernoulli trials the probability for success in the kth trial is Pk k = 1, 2..... The number of strings with a given number of failures between two subsequent successes is studied. Explicit expressions for distributions and moments are obtained for the case in which Pk = a/(a + b + k - 1), a > 0, b >= 0. Also, the limit behaviour of the longest failure string in the first n trials is considered. For b = 0, the strings correspond to cycles in random permutations.
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| 10. |
- Holst, Lars
(författare)
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ON CONSECUTIVE RECORDS IN CERTAIN BERNOULLI SEQUENCES
- 2009
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 46:4, s. 1201-1208
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Tidskriftsartikel (refereegranskat)abstract
- In an infinite sequence of independent Bernoulli trials with success probabilities p(k) = a/(a + b + k - 1) for k = 1, 2 3, ... , let N-r be the number of r >= 2 consecutive successes. Expressions for the first two moments of N-r are derived. Asymptotics of the probability of no occurrence of r consecutive successes for large r are obtained. Using an embedding in a marked Poisson process, it is indicated how the distribution of N-r can be calculated for small r.
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| 11. |
- Holst, Lars
(författare)
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The number of two consecutive successes in a Hoppe-Pólya urn
- 2008
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 45:3, s. 901-906
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Tidskriftsartikel (refereegranskat)abstract
- In a sequence of independent Bernoulli trials the probability of success in the kth trial is pk = a/(a + b + k - 1). An explicit formula for the binomial moments of the number of two consecutive successes in the first n trials is obtained and some consequences of it are derived.
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| 12. |
- Janson, Svante, et al.
(författare)
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The integral of the supremum process of Brownian motion
- 2009
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 46:2, s. 593-600
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study the integral of the supremum process of standard Brownian motion. We present an explicit formula for the moments of the integral (or area) A(T) covered by the process in the time interval [0, T]. The Laplace transform of A(T) follows as a consequence. The main proof involves a double Laplace transform of A(T) and is based on excursion theory and local time for Brownian motion.
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| 13. |
- Lindell, Andreas, et al.
(författare)
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Distributions of the longest excursions in a tied down simple random walk and in a Brownian bridge
- 2007
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 44:4, s. 1056-1067
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Tidskriftsartikel (refereegranskat)abstract
- Expressions for the joint distribution of the longest and second longest excursions as well as the marginal distributions of the three longest excursions in the Brownian bridge are obtained. The method, which primarily makes use of the weak convergence of the random walk to the Brownian motion, principally gives the possibility to obtain any desired joint or marginal distribution. Numerical illustrations of the results are also given.
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| 14. |
- Markström, Klas
(författare)
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Negative association does not imply log-concavity of the rank sequence
- 2007
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Ingår i: Journal of Applied Probability. - 0021-9002 .- 1475-6072. ; 44:4, s. 1119-1121
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Tidskriftsartikel (refereegranskat)abstract
- We present a minimum counterexample to the conjecture that a negatively associated random variable has an ultra-log-concave rank sequence. The rank sequence does not in fact even need to be unimodal.
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| 15. |
- Serra, Maria Conceicao, 1973
(författare)
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On the waiting time to escape
- 2006
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 43:1, s. 296-302
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Tidskriftsartikel (refereegranskat)abstract
- The mathematical model we consider here is a decomposable Galton-Watson process with individuals of two types, 0 and 1. Individuals of type 0 are supercritical and can only produce individuals of type 0, whereas individuals of type 1 are subcritical and can produce individuals of both types. The aim of this paper is to study the properties of the waiting time to escape, i.e. the time it takes to produce a type-0 individual that escapes extinction when the process starts with a type-1 individual. With a view towards applications, we provide examples of populations in biological and medical contexts that can be suitably modeled by such processes.
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| 16. |
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| 17. |
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| 18. |
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| 19. |
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| 20. |
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| 21. |
- Nordvall Lagerås, Andreas, et al.
(författare)
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Reduced branching processes with very heavy tails
- 2008
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Ingår i: Journal of Applied Probability. - 0021-9002. ; 45:1, s. 190-200
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Tidskriftsartikel (refereegranskat)abstract
- The reduced Markov branching process is a stochastic model for the genealogy of an unstructured biological population. Its limit behavior in the critical case is well studied for the Zolotarev-Slack regularity parameter α∈(0,1]. We turn to the case of very heavy tailed reproduction distribution α=0 assuming Zubkov’s regularitycondition with parameter β∈(0,∞). Our main result gives a new asymptotic pattern for the reduced branching process conditioned on non-extinction during a long time interval.
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