We consider fractional Brownian motion with D-dimensional time in the domain G(T)=(-T<ti<T,tj>0 if j<d+1). Let P(T) be the probability that the process will not exceed a fixed level in G(T). We show that for large T, logP(T)=(D-dH)logT(1+o(1)) where H is the Hurst parameter of the process
Suppose that a Brownian motion can only be observed after a random time τ . We are interested in the distribution of the time T required to record the first visit to a given threshold. The cases when τ has an exponential and an Erlang distribution are considered. A method to approximate the probability density function...
Mario Lefebvre, Ibrahim Touré· WSEAS Transactions on System...· 0 citations
We develop a general discrete approximation scheme for time-changed Brownian motions on $\mathbb{R}^d$. Our approximation scheme works for any smooth measure with full quasi-support on $\mathbb{R}^d$ with suitable initial distributions. Under some mild conditions on the smooth measure, the discrete approximation scheme...
We give a full characterization of the fixed points of Branching Brownian motion with critical and supercritical drifts under no additional assumptions besides it being locally finite almost surely. In particular, we do not assume finite intensity (Kabluchko, 2012) or the finite top particle (Chen-Garban-Shekhar, 2023)...
Xin-Xin Chen, Arnab Chowdhury, A. Shekhar et al.· 0 citations
We study stochastic systems driven by a Brownian sheet and formulate a Markov property adapted to their two-parameter structure. For time-space homogeneous It\^o sheets, the future evolution from a point $(t,x)$ is not determined by the single value $Y(t,x)$ alone, but also by the boundary data along the horizontal and...
N. Agram, Bernt Oksendal, F. Proske et al.· 0 citations
We consider scaling limits of integer-valued random walks whose transition probabilities are translation-invariant everywhere except on a set that we will call a membrane or an interface. If the jumps outside the membrane are i.i.d. mean-zero random variables with finite variance, then possible examples of the correspo...
This work studies parameter estimation for a stochastic process that combines a Brownian motion with trend and two fractional Brownian motions with distinct Hurst indices. The process is given by , where is a standard Brownian motion and are fractional Brownian motions with Hurst indices such that , with , and being m...
Phisitphong Ketrat, Raywat Tanadkithirun· Science & Technology Asi...· 0 citations
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