Discounted additive functionals of Markov processes
Discounted optimal stopping for maxima in diffusion models with finite horizon.
Discrete Löwner evolution
Discrete Models of Time-Fractional Diffusion in a Potential Well
Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.By generalization of Ehrenfest’s urn model, we obtain discrete approximations to spatially one-dimensional time-fractional diffusion processes with drift towards the origin. These discrete approximations can be interpreted (a) as difference schemes for the relevant time-fractional partial differential equation, (b) as random walk models. The relevant convergence questions as well as the behaviour for time tending to infinity...
Discrete small world networks.
Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations
Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems. This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time and state. The limit N → ∞ of an infinite population can be considered explicitly, generally leading to a replicator-type equation in zero order, and to a Fokker-Planck-type equation in first order in 1/√N. Consequences and relations to some previous approaches...
Discrete time markovian agents interacting through a potential
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition probability kernel that depends on the ‘gradient’ of the potential field. The particles, in turn, dynamically modify the potential field through their cumulative input. Interacting Markov processes of the above form have been suggested as models for active biological transport...
Discrete time nonlinear filters with informative observations are stable.
Discrete time risk sensitive portfolio optimization with consumption and proportional transaction costs
Risk sensitive and risk neutral long run portfolio problems with consumption and proportional transaction costs are studied. Existence of solutions to suitable Bellman equations is shown. The asymptotics of the risk sensitive cost when the risk factor converges to 0 is then considered. It turns out that optimal strategies are stationary functions of the portfolio (portions of the wealth invested in assets) and of economic factors. Furthermore an optimal portfolio strategy for a risk neutral control...
Discrete version of Dungey’s proof for the gradient heat kernel estimate on coverings
We obtain another proof of a Gaussian upper estimate for a gradient of the heat kernel on cofinite covering graphs whose covering transformation group has a polynomial volume growth. It is proved by using the temporal regularity of the discrete heat kernel obtained by Blunck [2] and Christ [3] along with the arguments of Dungey [7] on covering manifolds.
Discrete-time Markov control processes with discounted unbounded costs: Optimality criteria
Dislocation measure of the fragmentation of a general Lévy tree
Given a general critical or sub-critical branching mechanism and its associated Lévy continuum random tree, we consider a pruning procedure on this tree using a Poisson snake. It defines a fragmentation process on the tree. We compute the family of dislocation measures associated with this fragmentation. This work generalizes the work made for a Brownian tree [R. Abraham and L. Serlet, Elect. J. Probab. 7 (2002) 1–15] and for a tree without Brownian part [R. Abraham and J.-F. Delmas, Probab. Th....
Dislocation measure of the fragmentation of a general Lévy tree
Given a general critical or sub-critical branching mechanism and its associated Lévy continuum random tree, we consider a pruning procedure on this tree using a Poisson snake. It defines a fragmentation process on the tree. We compute the family of dislocation measures associated with this fragmentation. This work generalizes the work made for a Brownian tree [R. Abraham and L. Serlet, Elect. J. Probab.7 (2002) 1–15] and for a tree without Brownian part [R. Abraham and J.-F. Delmas, Probab. Th....
Distances in random graphs with finite mean and infinite variance degrees.
Distribution function inequalities for the density of the area integral
We prove good- inequalities for the area integral, the nontangential maximal function, and the maximal density of the area integral. This answers a question raised by R. F. Gundy. We also prove a Kesten type law of the iterated logarithm for harmonic functions. Our Theorems 1 and 2 are for Lipschitz domains. However, all our results are new even in the case of .
Distribution of the Brownian motion on its way to hitting zero.
Distributions of functionals of diffusions with jumps.
Distributions of sojourn time, maximum and minimum for pseudo-processes governed by higher-order heat-type equations.
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 iterated gradient and chaotic decompositions of Poisson jump times functionals.
We define a class of distributions on Poisson space which allows to iterate a modification of the gradient of [1]. As an application we obtain, with relatively short calculations, a formula for the chaos expansion of functionals of jump times of the Poisson process.