Some examples of solutions to an inverse problem for the first-passage place of a jump-diffusion process

2021/04/13 by Mario Abundo, Abundo, Mario
Biochemistry, Genetics and Molecular Biology · Mathematics · #60H05 #60H10 #60J60 #Diffusion and Search Dynamics #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2104.06385

openalex publication_date 2021/04/13 · openalex created_date 2022/08/12 · openalex updated_date 2026/07/28

Abstract

We report some additional examples of explicit solutions to an inverse first-passage place problem for one-dimensional diffusions with jumps, introduced in a previous paper. If X(t) is a one-dimensional diffusion with jumps, starting from a random position η∈ [a,b], let be τ_a,b the time at which X(t) first exits the interval (a,b), and π_a = P(X(τ_a,b) ≤ a) the probability of exit from the left of (a,b). Given a probability q ∈ (0,1), the problem consists in finding the density g of η (if it exists) such that π_a = q; it can be seen as a problem of optimization.

Related

• Inverse first-passage problems of a diffusion with resetting
• The inverse first-passage problem and optimal stopping
• An inverse optimal stopping problem for diffusion processes
• The first passage time problem for mixed-exponential jump processes with applications in insurance and finance
• First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes