Explicit formulae are found for the probability that the Brownian motion, Bt, up-crosses, in [0,
T], a piecewise-linear function S (t), with the condition that the value of Bt is assigned at a …

Let Y (t) be a one-dimensional jump-diffusion process and X (t) be defined by d X (t)= ρ [X (t),
Y (t)] dt, where ρ (·,·) is either a strictly positive or negative function. First-passage-time …

The LQG homing problem, in which a diffusion process is controlled until a certain event
takes place, is considered for Wiener processes with jumps that are exponentially …

We study the problem of the first passage time through a constant boundary for a jump
diffusion process whose infinitesimal generator is a nonlocal Jacobi operator. Due to the …

The problem of optimally controlling one-dimensional diffusion processes until they enter a
given stopping set is extended to the case of jump-diffusion processes. We assume that the …

The paper presents exact formulae related to the distribution of the first passage time τ x of
the jump-telegraph process. In particular, the Laplace transform of τ x is analysed, when a …

For a one-dimensional jump-diffusion process X (t), starting from x> 0, it is studied the
probability distribution of the area A (x) swept out by X (t) till its first-passage time below zero …

It is studied the first-passage time (FPT) of a time homogeneous one-dimensional diffusion,
driven by the stochastic differential equation dX (t)= μ (X (t)) dt+ σ (X (t)) dB t, X (0)= x 0 …

We study an inverse first-hitting problem for a one-dimensional, time-homogeneous diffusion
X (t) reflected between two boundaries a and b, which starts from a random position η. Let …

We consider the problem of optimally controlling a one-dimensional Wiener process with
Poissonian jumps until it leaves the interval [a, b]. The exact optimal control is obtained in a …