The law of geometric Brownian motion and its integral, revisited; application to conditional moments

C Donati-Martin, H Matsumoto, M Yor - … from the First World Congress of …, 2002 - Springer
The Law of Geometric Brownian Motion and its Integral, Revisited Application to Conditional
Moments Page 1 The Law of Geometric Brownian Motion and its Integral, Revisited …

Revisiting integral functionals of geometric Brownian motion

E Boguslavskaya, L Vostrikova - Statistics & Probability Letters, 2020 - Elsevier
In this paper we revisit the integral functional of geometric Brownian motion I t=∫ 0 te−(μ s+
σ W s) ds, where μ∈ R, σ> 0 and (W s) s> 0 is a standard Brownian motion. Specifically, we …

[引用][C] On the distribution properties of skew Brownian motion's local time

Y Lyulko - Workshop on Stochastic Methods in Financial Markets

[引用][C] On distributions of functionals of Brownian motion stopped at inverse range time

AN Borodin - Zapiski Nauchnykh Seminarov POMI, 1999 - mathnet.ru
AN Borodin, “On distributions of functionals of Brownian motion stopped at inverse range time”,
Probability and statistics. Part 3, Zap. Nauchn. Sem. POMI, 260, POMI, St. Petersburg, 1999 …

On some Brownian functionals and their applications to moments in the lognormal stochastic volatility model

J Jakubowski, M Wiśniewolski - Studia Mathematica, 2013 - infona.pl
We find a probabilistic representation of the Laplace transform of some special functional of
geometric Brownian motion using squared Bessel and radial Ornstein-Uhlenbeck …

Exact asymptotics of distributions of integral functionals of the geometric Brownian motion and other related formulas

VR Fatalov - Problems of Information Transmission, 2007 - Springer
We prove results on exact asymptotics of the probabilities P\left {∫\limits_0^ 1 e^ ε ξ (t) dt>
b\right\}, P\left {∫\limits_0^ 1 e^ ε| ξ (t)| dt> b\right\}, ε → 0, where b> 1, for two Gaussian …

Brownian Motion with a Singular Drift

D DeBlassie, A Oprisan, RG Smits - arXiv preprint arXiv:2403.06043, 2024 - arxiv.org
arXiv:2403.06043v1 [math.PR] 9 Mar 2024 Page 1 arXiv:2403.06043v1 [math.PR] 9 Mar
2024 Brownian Motion with a Singular Drift Dante DeBlassie Adina Oprisan Robert G. Smits …

On the distribution of the time-integral of the geometric Brownian motion

P Nándori, D Pirjol - Journal of Computational and Applied Mathematics, 2022 - Elsevier
We study the numerical evaluation of several functions appearing in the small time
expansion of the distribution of the time-integral of the geometric Brownian motion as well as …

On the distribution of estimators of diffusion constants for Brownian motion

D Boyer, DS Dean - Journal of Physics A: Mathematical and …, 2011 - iopscience.iop.org
We discuss the distribution of various estimators for extracting the diffusion constant of single
Brownian trajectories obtained by fitting the squared displacement of the trajectory. The …

[HTML][HTML] Approximating the first passage time density of diffusion processes with state-dependent jumps

G D'Onofrio, A Lanteri - Fractal and Fractional, 2022 - mdpi.com
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 …