Distribution of the Brownian motion on its way to hitting zero.
Distributions of truncations of the heat kernel on the complex projective space
Let be a Brownian motion valued in the complex projective space . Using unitary spherical harmonics of homogeneous degree zero, we derive the densities of and of , and express them through Jacobi polynomials in the simplices of and respectively. More generally, the distribution of may be derived using the decomposition of the unitary spherical harmonics under the action of the unitary group yet computations become tedious. We also revisit the approach initiated in [13] and based on...
Distribution-Valued Processes Arising from Independent Brownian Motions.
Domain perturbations, Brownian motion, capacities, and ground states of Dirichlet Schrödinger operators.
Dynamic portfolio optimization with risk management and strategy constraints
We investigate the problem of power utility maximization considering risk management and strategy constraints. The aim of this paper is to obtain admissible dynamic portfolio strategies. In case the floor is guaranteed with probability one, we provide two admissible solutions, the option based portfolio insurance in the constrained model, and the alternative method and show that none of the solutions dominate the other. In case the floor is guaranteed partially, we provide one admissible solution,...
Dynamic term structure modelling with default and mortality risk: new results on existence and monotonicity
This paper considers dynamic term structure models like the ones appearing in portfolio credit risk modelling or life insurance. We study general forward rate curves driven by infinitely many Brownian motions and an integer-valued random measure, generalizing existing approaches in the literature. A precise characterization of absence of arbitrage in such markets is given in terms of a suitable criterion for no asymptotic free lunch (NAFL). From this, we obtain drift conditions which are equivalent...
Dynamical semigroups and Markov processes on C*-algebras.
Dyson's Brownian motions, intertwining and interlacing.
Editorial - Spring School Mons Random differential equations and gaussian fields
Eigenvalue expansions for Brownian motion with an application to occupation times.
Eigenvalues of the Laguerre process as non-colliding squared Bessel processes.
Elementary stochastic calculus for finance with infinitesimals
The concept of an equivalent martingale measure is of key importance for pricing of financial derivative contracts. The goal of the paper is to apply infinitesimals in the non-standard analysis set-up to provide an elementary construction of the equivalent martingale measure built on hyperfinite binomial trees with infinitesimal time steps.
Embeddings in brownian motion
Entropy estimate for -monotone functions via small ball probability of integrated Brownian motions.
Equality cases in the symmetrization inequalities for Brownian transition functions and Dirichlet heat kernels.
Equation (1) et mélanges de lois normales
Equidistant sampling for the maximum of a Brownian motion with drift on a finite horizon.
Erratum to “The supremum of brownian local times on Hölder curves”
Escaping the Brownian stalkers.
Estimates of random walk exit probabilities and application to loop-erased random walk.