App Stochastic Processes

App Stochastic Processes Android (Java) application from IIG Technology for studying probabilistic (stochastic) processes: accurate formulas + Monte Carlo simulation + graphs, in 5 languages ​​(English by default, Bulgarian, Deutsch, Français, Español). ## Modules | Module | Accurate results | Simulation / graphs | | **Markov Chains** | classes, closed/transitive, period, πₙ = π₀Pⁿ, Pⁿ, stationary distribution, mean return time, fundamental matrix N = (I−Q)⁻¹, probabilities and time to absorption | trajectory, time shares vs π, evolution of πₙ | | **Random walk (ruining the player)** | P(reach N), P(ruin), expected duration, N = ∞ | trajectories, P(N) and E[T] as a function of initial capital | | **Poisson process** | P(N(T)=k), distribution function, Erlang/Gamma for the kth event | trajectories N(t), histogram vs theory, waiting density | | **Brownian motion / GBD / Ornstein–Uhlenbeck** | E, Var, 95% band, P(X(T) > x₀), median, half-life, stationary law | banded trajectories, histogram of X(T) vs density (exact discretization) | | **M/M/c/K Tails** | P₀, L, Lq, W, Wq, Erlang C, Erlang B / failure, load, Little's law | Gillespie simulation, N(t), pₙ theory vs simulation | | **Branching processes (Galton–Watson)** | m, Var, probability of degeneracy q (fixed point of f), P(degenerate to generation n), E[Zₙ], Var[Zₙ] | spider diagram, generational degeneracy, trajectories (log scale) | Each module has: theory (expandable), buttons with examples, generated form with parameters, single-width report (can be highlighted/copied), sharing results and graphs with Two-finger zoom, pan, and double-tap to return. `